Risk

Risk is the potential for harm. Although the concept of risk—and some of the same analytic tools—are also used in finance and actuarial science, as well as to describe threats from natural events, this discussion focuses on risks to human health and the environment from toxic pollution.

risk=f(hazard, exposure)

The magnitude and severity of risk are a function of the types of harm (i.e., the hazards, or what can go wrong) and the extent and likelihood of exposure. If the elements of hazard and exposure are not both in play, there is no biophysical risk to health or the environment. However, the perception of risk can be as damaging, with potential for destroying trust and sapping resources and emotional energy. Maintaining an appropriate balance between the level of social concern about a threat on the one hand and the extent of its social impact or risk on the other hand is an ongoing challenge for risk communicators, an engaged citizenry, and policymakers.

Hazards

Hazards to human health include cancers, asthma, skin rashes, infectious diseases, eye and lung irritation, developmental problems, and broken bones. Population hazards also include habitat destruction, resource degradation, threats to public health from contamination of drinking water, bacterial resistance to antibiotics, famine, and such macroconcerns as global climate change. Of greatest consequence are hazardous effects that are irreversible or long lasting, or which seriously compromise the length or quality of lives in current and future generations. Hazards that will affect future generations, or groups spatially removed from the root of the problem, may go unidentified or be discounted in formulating an assessment of risk.

The Dose–Response Concept

The toxicity or severity of a hazard can be described by a dose–effect (also called dose–response ) relationship. This concept is conveyed graphically by plotting dosage (amount or concentration of a toxin) against population.

Data for describing dose–response relationships are gathered from tests in which groups of organisms are exposed to a toxin at a range of doses. Typically, as the dose increases, the toxic effect of concern is produced in more of the population.

The dosage at which the specified effect is measured is called the effective dose (ED). The percentage of the population affected is indicated by a subscript. So for example, ED10 refers to the dose at which 10 percent of the population would be affected by the toxin. When the measured effect is mortality, the term lethal dose (LD) or lethal concentration (LC) is used. An LD50 is the dose at which 50 percent of a population is killed.

At the same dose, chemicals that are more hazardous affect a greater proportion of the population than do chemicals that are less hazardous. Thus chemicals that are less hazardous have a higher ED50 or LD50 than do those that are more hazardous.

While human beings are the population of ultimate interest in dose–response studies of human health hazards, rodents are typically used as surrogates in lab tests of the effects of the toxic materials. The process of extrapolating results from rodents (or other indicator organisms) to people introduces layers of uncertainty because of physiological, developmental, and size differences between the species. Hazardous effects on plants and animals are also studied using the same conceptual methods, both because of the intrinsic value of these species and also, in some cases, because they are indicators of indirect effects on the human population.

Population Variability

As dose–response relationships show, populations are not equally susceptible to toxic hazards. Differences among individuals are due to gender, age, inherited genetic makeup, and the wear and tear and immunities that develop during the course of life. For example some people have inherited the genes that enable them to detoxify certain pesticide poisons. These people do not get sick from exposure at levels that make other people ill. Current research is linking biomarkers for genetic risk factors to disease outcomes. As it becomes clearer why people are differently vulnerable (or resistant), it also becomes more apparent that the same risk-based standards may not be applicable across populations. For example dietary iron is a risk factor for heart disease among middle-aged men at concentrations considered beneficial to women of reproductive age.

Vulnerability to hazards also changes during our lifetimes, with greater sensitivity to many toxins during fetal development, the rapidly developing stages of early childhood, and puberty—although negative effects may not be manifest until much later in life. For these reasons, among others, exposures are not easily tied to disease outcomes (see sidebar). Just try to imagine, for example, how you or your parents would struggle to respond accurately to a survey asking which pesticides you were exposed to in early childhood, and in what quantities! Some toxins and infections are particularly hazardous to those with weakened immune systems and defenses, such as the elderly and those whose systems are compromised due to other diseases or by interactive effects with medical treatments or other chemical pollutants.

Exposure

Individuals are not at risk from the consequences of a hazard if they are not exposed to it. The critical factor linking exposure to risk is the quantity of toxin that is bioavailable to vulnerable organs or processes. However, bioavailability is difficult to measure directly, so various measurement endpoints are used as surrogates for exposure. For pesticides, these have included sales and use data, application dosages, residues on food, and fate-and-transport data (i.e., what happens to a pesticide after application, where it goes, and how fast it degrades). Exposures are sometimes estimated from mathematical or simulation models that extrapolate from data collected by empirical studies (e.g., the amount of pesticide reaching skin or clothing, tracked indoors on shoes, or leached through soil into groundwater).

Estimates of exposure can vary widely, depending on the method for collecting data, the surrogate indicator used, and whether the assumed range of possible exposures is limited to permitted quantities or also includes accidental or purposeful exposures at much higher levels.

Risk-Based Decisions

Whereas risk assessments are a product of the quality and choice of input data and the assumptions incorporated into the assessment model, the usefulness and relevance of a risk characterization depend largely on how the risk problem is perceived and formulated. A well-formulated problem must engage the perspectives of multiple "publics" and be integrated with decision-management options. Perceived options for risk management are constrained by societal values that determine what are considered acceptable risks and by the resources invested for risk mitigation (i.e., for preventing or remediating the problem).

The National Research Council framework for using risk to "inform decisions in a democratic society" (1996) iteratively builds from a multifaceted formulation of the problem incorporating all aspects of risk analysis. As defined by the Society for Risk Analysis, the premier professional organization in the field, these components include risk assessment—or the quantification and description of hazards and exposure, risk characterization, risk communication, risk management, and policy relating to risk. Criteria for a successful risk-based decision process are listed in the following table.

The assessment and regulation of sewage-sludge disposal provides a good illustration of the potential and foibles of risk-based decision making, underscoring the importance of a participatory and iterative analytical and deliberative process in setting risk standards and developing protective environmental policies.

Risks from Sewage Sludge: A Cross-Country Comparison

Sewage sludge is the semisolid or concentrated liquid residue generated during the treatment of wastewater. In addition to biodegradable organic material, sludges can contain pathogens (disease organisms) and industrial pollutants (such as heavy metals) that can be damaging to human health. Among the means for disposing of sludges—by incineration, landfilling, or spreading across farmland and other open space—only land application has the benefit of returning the fertilizing nutrients in sludge to the soil.

However, land application also has associated risks, including the long-term effects of increasing the concentration of nondegradable contaminants in the soil. These elements can be taken up into food plants, ingested by children who put soiled hands into their mouths, eroded into surface waters, or leached into groundwater.

The benefits and risks of sludge disposal accrue to different groups: The advantages of cheap disposal are reaped by those generating waste. The benefits from fertilizing nutrients are reaped by farmers and other land managers. Risks accrue to those who may ingest the toxins through the media of food, soil, water, or air, now and especially in the future, when toxins will have accumulated to higher levels.

In 1993 the U.S. Environmental Protection Agency established standards for land-application of sludge, setting limits for permitted quantities of nine pollutants—arsenic, cadmium, copper, lead, mercury, molybdenum, nickel, selenium, and zinc—on the basis of a risk assessment. A maximum

concentration load (MCL) per unit quantity of sludge was derived from an assessment of how much of each element a person could be exposed to in their lifetime without causing unacceptable harm. To calculate the MCL, assumptions were made about the body size of this person and what they would eat in the course of a lifetime (and therefore how much of each pollutant would be consumed). The model person used for the calculations was a young adult male who did not eat many vegetables (the food group that accumulates the heavy metals). Some therefore argue that this risk assessment is not sufficiently protective of children and of people who eat many vegetables or would otherwise be exposed to greater contaminant levels.

Several European countries (as well as Canadian provinces) have established more conservative standards, permitting only much lower contaminant levels in sludges that will be recycled through land application. The policy objective of these standards is to prevent the concentration of contaminants from accumulating above the level in soils where sludge has not been applied (i.e., above background levels). However, this approach lacks risk-based criteria, since background levels of contaminants vary greatly with the type of soil and how they have been used over time. (European soils have been the site of industrial and agricultural activities for centuries.)

It is entirely possible that comparably protective standards could have emerged in the United States from a risk-based policy that was more appropriately sensitive to vulnerable subpopulations, that incorporated protective buffers to compensate for current scientific uncertainties about the hazards of these elements, and that assumed higher levels of possible exposure through food, soil, and airborne particles.

The summary lesson to be taken from this comparison is that no matter what framework or assumptions are used—whether it be risk analysis or some other—decisions regarding health and the environmental protection are based on an intermixed combination of social values and science, neither of which is objective nor without uncertainty. While the view and measure of "risk" are not the same for all, the concept of "risk" remains meaningful and useful; "risk reduction" is a critical objective across all policy arenas; and the framework and tools of risk analysis offer a structured approach for evaluating, prioritizing, and acting on environmental and health issues.

Bibliography

Harrison, E.Z.; McBride, M.B.; and Bouldin, D.R. (1999.) "Land Application of Sewage Sludges: An Appraisal of the US Regulations." International Journal of Environment and Pollution 11(1):1–36.

National Research Council. (1996). Understanding Risk: Informing Decisions in a Democratic Society. Washington, D.C.: National Academy Press.

internet resources

Centers for Disease Control and Prevention. "Cancer Clusters." Available from http://www.cdc.gov/nceh/clusters.

Cornell University, Environmental Risk Analysis Program. "Links to Risk Analysis Resources & Organizations." Available from http://environmentalrisk.cornell.edu/ERAP/RiskLinks.cfm.

National Cancer Institute. "Cancer Clusters, Cancer Facts." Available from http://cis.nci.nih.gov/fact/3_58.htm.

Society for Risk Analysis. "Risk Glossary." Available from http://www.sra.org/glossary.htm.

Lois Levitan

CANCER CLUSTERS

When a number of people in a neighborhood or workplace develop the same disease within a short period of time, it may signal a disease cluster. A disease cluster is defined by having more cases of an illness within a particular geographic area and time period than would be statistically expected for a population with the same characteristics. Disease clusters can result from exposures to hazardous materials in the local environment or from similar lifestyle risk factors (i.e., people who live or work together may have similar eating, exercising, or smoking habits).

Disease clusters can provide clues to the cause—or risk factors—associated with a disease. They are easier to identify when a number of people show the same symptoms soon after exposure, such as when nausea follows soon after eating spoiled food in a restaurant. With a longer lag time or small number of sick people, or with symptoms that are dissimilar or not obvious, real disease clusters may not be noticed. Conversely, clusters may be suspected due to misperception of a higher-than-average incidence of cases, or when different diseases are perceived to be the same or to have stemmed from the same cause.

Cancer clusters are particularly difficult to prove because (1) there are more than one hundred types of cancer, each with different associated risk factors; (2) there is a typically long lag time between exposure to environmental risk factors and noticeable development of the cancer; and (3) the location of the suspected cluster may be different than where a diseased person lived, worked, or went to school at the time they were exposed. Cancer clusters are more likely to be identified if a large number of individuals are diagnosed with a rare cancer or one that is rare for their age group.

The "X" factor is a major stumbling block in communicating risk. Health standards are expressed in terms of 1 × 10–4 or 1 × 10–6. This is a shorthand way of expressing the increased number of deaths that exposure to the contaminant of concern is likely to cause over a given period of time. A 1 × 10–4 risk is a 1 in 10,000 (4 zeroes) risk; a 1 × 10–6 risk is a 1 in 1,000,000 risk. Since risk is dose (level of exposure) times time (length of exposure), a 30-year 1 × 10–6 health standard for cancer risk is the level of exposure that would be expected to cause one additional case of cancer in a population of one million people exposed at that level for 30 years.

RISK

For demographers, the risk of a demographically significant event–such as birth, death, the onset of illness, marriage, migration, or labor force entry or exit–is the probability that the event will occur. Demographically significant events define entry or exit from demographically significant conditions, such as life, death, residence in a politically defined region, various marital statuses, employment, and school enrollment.

The demographic definition of risk ignores the desirability and impact of risked events. For example, sexually-active women of childbearing age are "at risk" of pregnancy, but the demographer's calculation of that risk does not consider if women regard pregnancy with delight or dread. Nor does the demographer's risk evaluation consider differences between pregnancy that is unwanted due to minor timing inconveniences and pregnancy that is unwanted because it would precipitate the mother's death. In common language, negative consequences of events are losses and positive consequences are benefits. The demographic approach is technical. The technical analysis is sometimes simplified by calling the consequence of a risked event a loss; a benefit then is a negative loss.

Demographic Rates

Individuals are at risk of an event if and only if their risk exceeds zero. A demographic rate is a time-related measure of exposure to risk. The rate is measured by the number of occurrences of an event per at-risk person per unit time. If events are non-recurring (e.g., death), and the time interval for the measurement is one unit (e.g., a year), then the rate is the proportion of at-risk persons who experience the event per time period. In demography, rates at which an event occurs are distinguished from proportions of population segments who experience the event. The denominator of the proportion, but not the denominator of the rate, may include persons who are not at risk (e.g., men are not at risk of giving birth).

Rates are used to calculate or estimate important time-related measures, including the extent to which members of a population who enter a demographically significant state remain in it over time, the probabilities that an individual who enters that state will remain in it for various numbers of consecutive time periods, and the expected or mean future time remaining in a state for persons who already have been in the state a particular length of time. These measures include the so-called life-table quantities: age-specific death rates, age-specific expected length of remaining life, and proportion of the population surviving at each specific age.

Age-specific rates for a population are often applied to hypothetical or standard age distributions to compute standardized or adjusted rates, life expectancies, and other quantities for the entire population. Alternatively, hypothetical or standard rates are applied to the observed age distribution of a population to produce adjusted rates and expectancies for population aggregates.

Methods of Analysis

Risks can be simple or competing. For example, employed persons are at risk of job loss from mortality, retirement, layoff, mandatory military service, incarceration, and voluntary job termination; employed persons who leave their jobs by dying cannot also leave by retirement, layoff, or any other means. Competing risks are used to produce multiple decrement life tables in which members of a population can exit a demographic condition via several specified, mutually exclusive routes (e.g., one can exit the civilian non-institutionalized population by mortality, emigration, or institutionalization). Demographic risk analysis often focuses on socioeconomic differentials in exposure to risk of death and other demographically significant events, implicitly examining the effects on mortality of socioeconomic factors such as schooling, occupation, and race.

Because of practical limitations on the size of available datasets, empirical analysis of many socioeconomic differentials in risk requires multivariate statistical methods. Methods such as logit and probit analysis can be applied in some situations involving a risked event that can occur only once. Poisson regression methods are useful in those situations when the event can occur more than once. Multinomial logit and multinomial probit methods are useful in those situations when there are competing risks, only one of which can occur, and only once. For data that gives the duration of spells (uninterrupted periods spent in a demographic state of interest) various types of survival analysis methods are useful, including those based on exponential, Weibull, lognormal, and loglogistic distributions. Cox's proportional hazard method is frequently useful. Appropriate methods also appear in the literature on event history analysis.

Risk and Loss

Effective design of government policy and business strategy often requires prognostications of (a) future demographic risks, rates and proportions, and (b) the exposure to losses (i.e., costs and benefits) that would be associated with these risks, rates, and proportions, if they occurred as projected. The future or past size and age distribution of a population in a demographically significant condition can be projected or estimated by application of a set of age-specific survival rates to the current age-distribution of that population. In practice, all estimates and projections necessarily are based on a combination of information and conjecture about past, current, and sometimes future risks and other factors. Data limitations and methodological disputes add uncertainty. A common but incomplete response to this uncertainty is to make demographic projections in sets, each element of which is based on different assumptions about unknown information. But demography offers no standard procedures for choosing among the members of a set of projections, and the choice is inescapably subject to dispute. Production of a set of projections saves the demographer from the need to defend intrinsically-subjective speculation about the unknown, and it pushes disputes about demographic projections outside of demography.

The loss distribution. If it is possible to evaluate the losses associated with demographic events, then it is possible and often useful to evaluate the general level of exposure to loss from a set of risks, or from different subsets of those risks. Common descriptive statistics in addition to the mean and variance are informative but not routinely used. The expected loss is the first moment of the loss distribution, otherwise known as its mean or expectation. If outcomes x are continuously differentiable and occur with probability Pr(x) and loss L), then the expected loss, E), is given by E(L) = ∫x)Pr(x)dx. If outcomes are discrete, then E(L) = Σ_iL(x)Pr(x_i). The variance of) describes the accuracy with which loss can be anticipated without additional predictive information. The higher the variance, the less informative is the mean about the loss that one is likely to experience. The worst case loss is the maximum of the loss distribution.

In the absence of concrete knowledge about the future, insurance provides a defense against disruptively large losses and, more generally, a hedge against variance in the distribution of losses. Insurance permits individuals to experience some present loss with certainty (in the form of payment of premiums) in exchange for protection against uncertain future losses that exceed a threshold (the insurance deductible). Insurance commonly is available for only some risked events; for those that cannot be insured, the analysis of risk and loss exposure, and planning on the basis of that analysis, is particularly useful.

Valuing losses. Demography itself is seldom, if ever, informative about how to compare different types of losses. Comparison of dissimilar losses requires a theory of value, or at least some principles about how to compare dissimilar demographic states and the events, such as birth, death, employment, and migration that cause them to change. For example, how is one to compare the losses associated with 100 deaths from workplace injuries to job loss by 60,000 employed persons? Numerous and conflicting economic, legal, aesthetic, emotional, political, religious, and other analyses of value exist. Thus, disputes are endemic to considerations of the losses associated with demographic projections. Policies are often evaluated on their actual or projected effects on mortality and other demographically significant events. These disputes are especially severe when they concern social policies that involve tradeoffs between risks of different types, such as increased unemployment risk and increased mortality risk.

Conflicts also often focus on risk (probability) estimation and worst case analysis. The worst imaginable event in any situation is likely to be the demographic tragedy of massive loss of human life. Imaginable events are not necessarily possible. Because the demographic framework examines risk only for those who are at risk, the first question is whether or not the risk of the worst imaginable event is zero or so close to zero that it should be treated as such. If this risk is distinguishable from zero, then this loss is the worst case loss. But if this risk is not distinguishable from zero, then this loss passes out of consideration. Heated debate over the risk of the worst imaginable event has been a prominent feature of public policy discussion concerning nuclear power, genetically modified plants and animals, environmental pollution, workplace safety, and other matters.

Expert Versus Popular Views of Risk

Much of the disagreement between experts and the lay public appears to stem from, or to be exacerbated by, the following:

Differences in probability estimation. Lacking technical training and often distrustful of expert pronouncements, substantial proportions of the lay public seem to prefer their own subjective estimates of risk probabilities to the data-based estimates of technical experts. A substantial segment of the population appears to lack intuitive understanding of very small decimal fractions, with consequent difficulty understanding the frequency of occurrence of low-probability events.

Differences in valuation of risked events. Experts tend to focus on quantitative loss measures and tend to use generally accepted estimation methods. In contrast, large segments of the general public rely on subjective evaluations that are quite dissimilar to expert evaluations.

Differences in attention. There are differences in attention given to the worst imaginable loss versus the average, expected, or most-likely loss. Attentive to the accuracy of their predictions over the long run, technical experts tend to give the greatest weight to scenarios that are most likely, and no weight to scenarios that have no probability of occurrence. Substantial segments of the general public focus on the worst imaginable case, perhaps because it inspires the greatest emotional response.

Differences in the conceptualization of losses. At their best, risk experts apply methods that let them make finely-graded comparisons of the losses associated with the occurrence of a risked event to the losses associated with its nonoccurrence. For example, technologies periodically fail disastrously, and disasters take lives (e.g., airplanes crash, bridges collapse, and physician errors kill patients). A simple and popular measure of the impact of technology failure is the number of lives lost from it. But technologies that fail periodically also can prolong and improve the quality of lives. At a minimum, one should compare the number of lives lost from a technology failure to the number of lives that would have been lost if the technology had not been deployed at all. And since everyone dies eventually, regardless of what technology is or is not deployed, the relevant measure is even better approximated by the number of person-years of life lost by the failure of a technology, compared to the number of person-years of life that would be lost by not deploying that same technology. Technical experts can apply life tables or analogous methods to calculate the loss of person-years of remaining life. Analysis and comparison of age-specific death rates (rather than numbers of deaths) is yet more complicated and directs attention to the societal rather than the individual consequences of deadly events. Quality-of-life issues are important too.

Differences in considerations of "spillover" effects. Experts tend to confine their analyses to variables that they can measure; substantial segments of the general public appear to consider the consequences of a risked event on their entire way of life. Losing a job can be seen as a simple loss of income, or it can be seen as the unraveling of everything supported by that income in the family of the employed person.

Differences in treatment of losses associated with unfamiliar risks. Substantial portions of the general public appear to respond to danger from an unfamiliar event (e.g., anthrax infection by contaminated mail, real or imagined illness from radiation-sterilized food) by increasing their estimate of the risk (probability) of experiencing the event, increasing their estimate of the loss that would result from the experience, or both, sometimes with anxiety, hostility, and the growth of social movements and collective action added.

Differences between technical and lay approaches to risk and loss exposure lead to questions about when it is useful to apply the technical analysis to public policy debates, and how to present it to those who combine high emotional interest in the subject with low exposure to the technical issues. Answers to these questions are external to demography, and they rest on judgments and strategic decisions about what is worth studying in detail, and what social choice inferences should be emphasized, stated, or left implicit. Widely-felt emotions and subjective impressions are social facts that cannot be ignored, but they are poor tools for analysis of risk and loss exposure. Those who claim that risk and loss exposure are equivalent to the general public's perception of them risk seriously flawed results.

Equally unstable analyses may result from the so-called rival rationalities view that conceives of experts as focused narrowly on statistical analysis of that which can be quantified, and an equally rational general public focused on a wide range of qualitative aspects of risk, including voluntariness and fairness of risk and loss exposure, and the dread with which a possible loss is perceived. The rival rationality view of risk assessment is not subject to any requirement for empirical evidence on risk magnitudes. This method is likely to be particularly troublesome when the risks of advanced technologies are considered. When science is misunderstood, as it often is, then popular misconceptions can and do lead to perceptions of imagined risks involving horrible but imaginary future losses. Finally, there appears to be confusion regarding the perceptions that are the basis for lay assessments of risk and loss exposure: It has been argued that anxiety about a risked event makes exposure to that event seem less voluntary, thereby raising the perceived risk of the event and exposure to loss from it, regardless of any actual difference in risk or exposure.

Conclusion

In summary, demography offers a particular conceptual and methodological framework for the measurement and analysis of risk; for predicting, forecasting, and comparing risks in different times and places; and for understanding how a given risk structure affects a population. The demographic approach to risk emphasizes the explicit connection between the structure of risk experienced by a population and the structure of age–the time spent in a demographically significant condition–that the population develops over time.

Demographic techniques emphasize the proper technical calculation of demographic risk measures. Demographic methods permit and even encourage analysis based on hypothetical values of demographic risks. These calculations are an important step in the analysis of exposure to loss. But demography offers no guidance about how to value the losses (and benefits) associated with the occurrence of risked events. Thus, demographic analysis of loss exposure requires combining demographic risk calculation with loss evaluations provided by other disciplines, engendering all the difficulties described above.

See also: Accidents; Disasters; Life Tables; Event History Analysis; Value of Life, Economic.

bibliography

Margolis, Howard. 1996. Dealing with Risk. Chicago: University of Chicago Press.

Preston, Samuel, Patrick Heuveline, and Michel Guillot. 2001. Demography: Measuring and Modeling Population Processes. Oxford, Eng. and Malden, MA: Blackwell Publishers.

Slovic, Paul. 2000. The Perception of Risk. Earthscan Publications.

Timmreck, Thomas. 1994. An Introduction to Epidemiology. Boston, MA, and London: Jones and Bartlett.

Ross M. Stolzenberg

Howard Margolis

Risk

RISK, UNCERTAINTY, AND PERCEPTION

RISK IN ECONOMICS

RISK IN OTHER SOCIAL SCIENCES

BIBLIOGRAPHY

The concept of risk is fundamental in the social sciences. Risk appears in numerous guises, from theoretical modeling of financial decisions to determining the social consequences of expanded nuclear power usage. Despite this importance, the precise definition of risk depends on the context and application. Common usage is derived from insurance applications where risk represents the possibility of loss, injury, or peril. This definition is reflected in various risk assessment and management applications, ranging from social and psychological risk to environmental and biohazard risk, where units of measurement for risk vary with context. In contrast, financial economics associates risk with the possibility that the actual return for a security will differ from the expected return. This financial risk is typically measured using the variance or standard deviation of historical return from the mean return, a definition of risk that includes both positive and negative outcomes. Key theoretical notions such as risk aversion and the risk-return tradeoff employ this definition. Where only the possibility of financial loss is of concern, as in value-at-risk applications, measurements are evaluated using the left tail of the relevant probability distribution.

RISK, UNCERTAINTY, AND PERCEPTION

The evolution of methods for the identification, assessment, and management of risk have played a central role in the progress of civilization. In ancient times, religious beliefs were important in reconciling the risks confronting a society. Appeals to the gods by the priesthood, prophecies from the oracle, and chanting by the shaman were all methods of passively dealing with risks encountered. The development of scientific, mathematical, and probabilistic methods during the Enlightenment permitted risk to be more actively identified and assessed. This advancement encountered a philosophical quandary concerning subjective and objective interpretations of probability. More precisely, the objective interpretation views probability as inherent in nature. Logic, scientific investigation, and statistical analysis can be used to discover objective probabilities. In contrast, subjective probabilities quantify an individual’s belief in the truth of a proposition or the occurrence of an event and are revealed in an individual’s choice behavior. Such probabilities can vary among individuals due, for instance, to differing degrees of ignorance about the event of interest.

Debate over subjective versus objective probability reached a peak around the time that Frank Knight (1885–1972) introduced a distinction between risk—where the objective probability of an event is at least measurable—and uncertainty, where the probability is not knowable and has to be determined subjectively. This terminological distinction between risk and uncertainty has now faded from common usage as the subjectivist approach has gained prominence, supported by seminal contributions from Frank Ramsey (1903–1930), Bruno di Finetti (1906–1985), and Leonard Savage (1917–1971). Attention has shifted to whether subjective beliefs derive from intuition or are realized only in choice behavior. The intuitive approach leads to a focus on the perception of risk, a concept often employed in psychometric and sociological research. Development of the choice-theoretic approach to subjective probability was facilitated by the expected utility function introduced by John von Neumann (1903–1957) and Oskar Morgenstern (1902–1976) in a classic work of social science, The Theory of Games and Economic Behavior (1944). The choice-theoretic approach has sustained the modeling of decision-making under uncertainty that is a central component of modern economic theory.

RISK IN ECONOMICS

Prior to von Neumann and Morgenstern, mathematically formal neoclassical economic theory was based on certainty or perfect foresight. Consideration of risk in decision-making could be found in the less formal approaches of Frank Knight, John Maynard Keynes (1883–1946), and Irving Fisher (1867–1947) that have contributed to a range of future contributions and perspectives on the impacts of risk in economics. Knight’s recognition that uncertainty could be handled by the insurance principle led to contributions on the importance of moral hazard and adverse selection in decision-making under uncertainty. By explicitly recognizing what he termed the “caution coefficient,” which measures the difference between the mathematical expectation and the price that will be paid for a gamble, Fisher laid the foundation for later contributions in mean-variance portfolio theory. The numerous contributions by Keynes on risk and uncertainty range from the Treatise on Probability (1921) to the General Theory of Employment, Interest and Money (1936). Disciples of Keynes, such as George L. S. Shackle (1903–1992) argue against the use of probability theory to model decision-making under uncertainty. Similarly, the failings of the ergodicity assumption are an important post-Keynesian critique of mathematically formal economic theory.

In addition to the diverse approaches to risk generated by Knight, Keynes, and Fisher, the application of mathematical formalism in economic theory has also produced impressive progress. Using preference orderings over state contingent commodities, Kenneth Arrow (born 1921) and Gerard Debreu (1921–2004) were able to extend the neoclassical economics of Stanley Jevons (1835–1882), Léon Walras (1843–1910) and Alfred Marshall (1842–1924) to include decision-making under uncertainty. This development follows naturally from using the choice-theoretic approach to subjective probability developed by von Neumann and Morgenstern. The utility of a certain outcome is replaced by the expected utility, calculated using known probabilities and the utilities for a set of random outcomes. The known probabilities are notionally determined by direct observation of previous choice behavior. Using this approach, while there is no formal distinction between risk and uncertainty, risk is usually associated with the variability of random outcomes and uncertainty with randomness. Sensitivity to risk is measured by comparing a certain outcome to a random outcome with the same expected value. Risky outcomes are measured in income, dollars, or returns, and can take both positive and negative values.

In financial economics, the expected utility framework has been applied to the problem of determining how to optimally combine individual securities into a portfolio of securities. Using an expected utility function specified over the expected portfolio return and variance of portfolio return, Harry Markowitz (born 1927) and William Sharpe (born 1934) were able to demonstrate that the variability or risk of a portfolio can be further divided into two components: firm specific risk, which is diversifiable and non-systematic; and market related risk, which is systematic and not diversifiable. Applying this to the tradeoff between risk and return, it is demonstrated that only increases in the systematic risk of an individual security will be rewarded with higher expected return. Hence, it is only that portion of the total variability of a security’s return that cannot be diversified away that warrants higher expected return. A measure of systematic risk—the beta of a security—is provided. Beta can be calculated as the slope coefficient in a least squares regression of individual security return on market return: the ratio of the covariance between the individual security return and the market return divided by the variance of the market return. More recently, a variety of risk measures have been developed to deal with limitations of variance of return and beta. These new measures include expected regret, conditional value at risk, and expected shortfall.

RISK IN OTHER SOCIAL SCIENCES

In social sciences other than economics, risk is usually identified with only negative outcomes. Units of measurement vary and can include the annual death toll, deaths or injuries per hour of exposure, loss of life expectancy, loss of working hours, accidents per mile driven, and crop loss per storm. A wide range of risk definitions and risk models are employed, including the classical approach based on objective probabilities, adapted from engineering and medicine; the choice-theoretic expected utility approach employed in economics; and the risk perception approach popular in sociology and psychometrics, where it is explicitly recognized that risk depends on cultural and individual perceptions that can differ from expert or objectively specified risk estimates. Because a variety of different negative outcomes can be of interest, measures of risk vary with the consequences involved. For example, in the classical approach, risk is defined as the loss or hazard if the event occurs times the probability the event will occur. In other words, risk is a combination of exposure and uncertainty. However, when risk involves an event such as death, then risk relates only to the probability of the event occurring.

In many situations in the social sciences, the application of objective probabilities to determine risk is problematic. Though it is possible to specify the relative frequency of a negative outcome from past data, the data is often limited and the estimated risk can be less than objective. In addition, because risk depends on the context, there is room for disagreement over the selection and measurement of relevant consequences. This poses problems in studies of perceived risk where individual perceptions are compared with calculated risk obtained from expert or objective estimates. Early studies on risk perception were concerned with determining whether there were significant deviations between individual risk perceptions and expert estimates. If such deviations were present, this provided support for the presence of heuristics and other sources of probability judgment bias. Further research has revealed that risk perception is a more complicated phenomenon. For example, risk perception depends on the target selected. This is manifested in risk denial, where individuals perceive risk to the general public from, say, alcohol or nuclear waste, to be greater than perceived risk to the individual or the individual’s family.

SEE ALSO Economics, Post Keynesian; Expected Utility Theory; Insurance; Keynes, John Maynard; Markowitz, Harry M.; Risk Neutrality; Risk Takers; Risk-Return Tradeoff; Utility, Von Neumann-Morgenstern; Von Neumann, John

BIBLIOGRAPHY

Arrow, Kenneth J. 1965. Aspects in the Theory of Risk Bearing. Helsinki: Yrjö Jahnssonin Säätiö.

Bernstein, Peter L. 1996. Against the Gods: The Remarkable Story of Risk. New York: John Wiley.

Fischhoff, Baruch, Stephen R. Watson and Chris Hope. 1984. Defining Risk. Policy Sciences 17 (2): 123–139.

Holton, Glyn A. 2004. Defining Risk. Financial Analysts Journal 60 (6): 19–25.

Karni, Edi. 1996. Probabilities and Beliefs. Journal of Risk and Uncertainty 13 (3): 249–262.

Poitras, Geoffrey. 2002. Risk Management, Speculation and Derivative Securities. Boston: Academic Press.

Slovic, Paul. 1987. Perception of Risk. Science 236 (April): 280–285.

Szegö, Giorgio. 2005. Measures of Risk. European Journal of Operational Research 163 (1): 5–19.

Geoffrey Poitras

risk / risk/ • n. a situation involving exposure to danger: flouting the law was too much of a risk | all outdoor activities carry an element of risk. ∎  [in sing.] the possibility that something unpleasant or unwelcome will happen: reduce the risk of heart disease | [as adj.] a high consumption of caffeine was suggested as a risk factor for loss of bone mass. ∎  [usu. in sing.] a person or thing regarded as likely to turn out well or badly, as specified, in a particular context or respect: Western banks regarded Romania as a good risk. ∎  a person or thing regarded as a threat to something in need of protection: she's a security risk. ∎  a thing regarded as likely to result in a specified danger: gloss paint can burn strongly and pose a fire risk. ∎  (usu. risks) a possibility of harm or damage against which something is insured. ∎  the possibility of financial loss: [as adj.] project finance is essentially an exercise in risk management. • v. [tr.] expose (someone or something valued) to danger, harm, or loss: he risked his life to save his dog. ∎  act or fail to act in such a way as to bring about the possibility of (an unpleasant or unwelcome event): unless you're dealing with pure alcohol you're risking contamination from benzene. ∎  incur the chance of unfortunate consequences by engaging in (an action): he was far too intelligent to risk attempting to deceive her.PHRASES: at risk exposed to harm or danger: 23 million people in Africa are at risk from starvation.at one's (own) risk used to indicate that if harm befalls a person or their possessions through their actions, it is their own responsibility: they undertook the adventure at their own risk.at the risk of doing something although there is the possibility of something unpleasant resulting: at the risk of boring people to tears, I repeat the most important rule in painting.at risk to oneself (or something) with the possibility of endangering oneself or something: he visited prisons at considerable risk to his health.risk one's neck put one's life in danger.run the risk (or run risks) expose oneself to the possibility of something unpleasant occurring: she preferred not to run the risk of encountering his sister.take a risk (or take risks) proceed in the knowledge that there is a chance of something unpleasant occurring.ORIGIN: mid 17th cent.: from French risque (noun), risquer (verb), from Italian risco ‘danger’ and rischiare ‘run into danger.’

risk A quantity derived both from the probability that a particular hazard will occur and the magnitude of the consequence of the undesirable effects of that hazard. The term risk is often used informally to mean the probability of a hazard occurring. See also tolerable risk.